12n
0053
(K12n
0053
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 11 10 12 4 7 9 11
Solving Sequence
6,11 4,7
3 10 8 9 12 1 2 5
c
6
c
3
c
10
c
7
c
9
c
11
c
12
c
1
c
5
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h291u
21
− 1049u
20
+ ··· + 2048b + 307, 1007u
21
− 2141u
20
+ ··· + 4096a − 3617,
u
22
− 2u
21
+ ··· + 11u
2
+ 1i
I
u
2
= h194087126632u
17
+ 1704357838964u
16
+ ··· + 10770316588487b + 37991651925802,
− 107427678939090u
17
− 569643045714954u
16
+ ··· + 786233110959551a − 1104507859905079,
u
18
+ 5u
17
+ ··· + 286u + 73i
I
u
3
= h−a
4
− a
3
u + a
3
+ 2a
2
u + 4au + 4b + 4a − 4, a
5
+ a
4
u − a
4
− 2a
3
u − 4a
2
u − 4a
2
+ 4a − 4u + 4, u
2
+ 1i
I
u
4
= hb − 2a, 4a
2
+ 2a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 52 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h291u
21
− 1049u
20
+ · · · + 2048b + 307, 1007u
21
− 2141u
20
+ · · · +
4096a − 3617, u
22
− 2u
21
+ · · · + 11u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−0.245850u
21
+ 0.522705u
20
+ ··· + 0.581787u + 0.883057
−0.142090u
21
+ 0.512207u
20
+ ··· − 0.498535u − 0.149902
a
7
=
1
u
2
a
3
=
−0.387939u
21
+ 1.03491u
20
+ ··· + 0.0832520u + 0.733154
−0.142090u
21
+ 0.512207u
20
+ ··· − 0.498535u − 0.149902
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
1
0.0156250u
21
− 0.0156250u
20
+ ··· + 0.0156250u + 0.0156250
a
12
=
−u
−0.0156250u
21
+ 0.0468750u
20
+ ··· + 0.984375u + 0.0156250
a
1
=
−u
−0.0156250u
21
+ 0.0468750u
20
+ ··· + 0.984375u + 0.0156250
a
2
=
−0.0476074u
21
+ 0.0178223u
20
+ ··· − 6.07739u + 0.889893
−0.0629883u
21
+ 0.0327148u
20
+ ··· − 0.0932617u − 0.125488
a
5
=
−0.118896u
21
+ 0.344971u
20
+ ··· − 0.420166u + 0.744385
−0.435059u
21
+ 0.703613u
20
+ ··· − 1.04932u − 0.661621
(ii) Obstruction class = −1
(iii) Cusp Shapes =
16767
8192
u
21
−
31037
8192
u
20
+ ··· +
76033
8192
u +
27071
8192
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 10u
21
+ ··· − u + 16
c
2
, c
5
u
22
+ 2u
21
+ ··· + 15u + 4
c
3
u
22
− 2u
21
+ ··· + 663u + 676
c
4
, c
9
u
22
+ 3u
21
+ ··· + 120u + 32
c
6
, c
7
, c
8
c
10
, c
11
u
22
+ 2u
21
+ ··· + 11u
2
+ 1
c
12
u
22
− 30u
21
+ ··· − 22u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 6y
21
+ ··· − 1857y + 256
c
2
, c
5
y
22
+ 10y
21
+ ··· − y + 16
c
3
y
22
+ 2y
21
+ ··· + 1664143y + 456976
c
4
, c
9
y
22
+ 5y
21
+ ··· − 1216y + 1024
c
6
, c
7
, c
8
c
10
, c
11
y
22
+ 30y
21
+ ··· + 22y + 1
c
12
y
22
− 78y
21
+ ··· + 102y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615782 + 0.803264I
a = −0.547833 − 0.548126I
b = 1.219690 − 0.593054I
−3.37145 + 2.38944I −5.45481 − 0.71996I
u = 0.615782 − 0.803264I
a = −0.547833 + 0.548126I
b = 1.219690 + 0.593054I
−3.37145 − 2.38944I −5.45481 + 0.71996I
u = 1.046550 + 0.353921I
a = 0.455127 + 0.346832I
b = 0.134390 + 0.768351I
−1.70749 − 1.42840I −2.82321 − 4.75814I
u = 1.046550 − 0.353921I
a = 0.455127 − 0.346832I
b = 0.134390 − 0.768351I
−1.70749 + 1.42840I −2.82321 + 4.75814I
u = 0.282269 + 0.708144I
a = −0.640971 − 0.473149I
b = 1.246260 + 0.317348I
−3.66689 − 5.42682I −7.22851 + 8.75440I
u = 0.282269 − 0.708144I
a = −0.640971 + 0.473149I
b = 1.246260 − 0.317348I
−3.66689 + 5.42682I −7.22851 − 8.75440I
u = 0.344516 + 0.519144I
a = 0.672348 + 0.637144I
b = −0.738214 − 0.182816I
−0.71829 − 1.39692I −3.45104 + 5.22381I
u = 0.344516 − 0.519144I
a = 0.672348 − 0.637144I
b = −0.738214 + 0.182816I
−0.71829 + 1.39692I −3.45104 − 5.22381I
u = −0.008200 + 0.342361I
a = 1.46314 + 0.68949I
b = −0.072113 − 0.750151I
0.55339 − 1.37498I 1.51135 + 4.45596I
u = −0.008200 − 0.342361I
a = 1.46314 − 0.68949I
b = −0.072113 + 0.750151I
0.55339 + 1.37498I 1.51135 − 4.45596I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21154 + 1.66696I
a = 0.133816 + 1.107720I
b = −0.091644 − 1.122210I
9.07448 + 4.87395I −0.77042 − 2.44706I
u = −0.21154 − 1.66696I
a = 0.133816 − 1.107720I
b = −0.091644 + 1.122210I
9.07448 − 4.87395I −0.77042 + 2.44706I
u = −0.221701 + 0.205211I
a = −2.25437 − 0.26322I
b = −0.678597 + 0.748849I
−0.25879 + 2.47978I 1.67019 − 4.37089I
u = −0.221701 − 0.205211I
a = −2.25437 + 0.26322I
b = −0.678597 − 0.748849I
−0.25879 − 2.47978I 1.67019 + 4.37089I
u = 0.10555 + 1.78725I
a = 0.354067 + 1.025410I
b = −1.93664 − 1.43012I
14.0985 − 4.5775I 1.42593 + 2.45051I
u = 0.10555 − 1.78725I
a = 0.354067 − 1.025410I
b = −1.93664 + 1.43012I
14.0985 + 4.5775I 1.42593 − 2.45051I
u = −0.50678 + 1.71782I
a = 0.038804 + 1.316300I
b = 1.79372 − 1.43052I
14.3505 + 13.9596I 0.89017 − 6.70291I
u = −0.50678 − 1.71782I
a = 0.038804 − 1.316300I
b = 1.79372 + 1.43052I
14.3505 − 13.9596I 0.89017 + 6.70291I
u = −0.41437 + 1.78716I
a = −0.115876 − 1.281550I
b = −1.17420 + 1.93112I
16.3189 + 7.7022I 2.88848 − 2.54222I
u = −0.41437 − 1.78716I
a = −0.115876 + 1.281550I
b = −1.17420 − 1.93112I
16.3189 − 7.7022I 2.88848 + 2.54222I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03207 + 1.84087I
a = −0.308249 − 1.105700I
b = 1.29737 + 1.95650I
16.1897 + 1.7866I 3.21686 − 1.63436I
u = −0.03207 − 1.84087I
a = −0.308249 + 1.105700I
b = 1.29737 − 1.95650I
16.1897 − 1.7866I 3.21686 + 1.63436I
7
II. I
u
2
= h1.94 × 10
11
u
17
+ 1.70 × 10
12
u
16
+ · · · + 1.08 × 10
13
b + 3.80 ×
10
13
, −1.07 × 10
14
u
17
− 5.70 × 10
14
u
16
+ · · · + 7.86 × 10
14
a − 1.10 ×
10
15
, u
18
+ 5u
17
+ · · · + 286u + 73i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
0.136636u
17
+ 0.724522u
16
+ ··· + 14.2921u + 1.40481
−0.0180206u
17
− 0.158246u
16
+ ··· − 14.7293u − 3.52744
a
7
=
1
u
2
a
3
=
0.118615u
17
+ 0.566276u
16
+ ··· − 0.437161u − 2.12263
−0.0180206u
17
− 0.158246u
16
+ ··· − 14.7293u − 3.52744
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−0.00986059u
17
− 0.0511795u
16
+ ··· + 8.20061u + 0.548839
0.0496987u
17
+ 0.246630u
16
+ ··· + 1.25653u − 0.863009
a
12
=
−0.0155752u
17
− 0.0281774u
16
+ ··· − 6.23377u − 3.19799
−0.00374040u
17
− 0.0370439u
16
+ ··· − 8.70788u − 2.90818
a
1
=
−0.0155752u
17
− 0.0281774u
16
+ ··· − 6.23377u − 3.19799
−0.00187659u
17
+ 0.0403158u
16
+ ··· + 4.36897u + 0.719823
a
2
=
−0.0396317u
17
− 0.119184u
16
+ ··· − 18.5066u − 5.67176
−0.0717938u
17
− 0.280007u
16
+ ··· + 7.64298u + 2.57570
a
5
=
0.0918527u
17
+ 0.479986u
16
+ ··· + 6.01042u − 2.13207
0.0272186u
17
+ 0.0921641u
16
+ ··· − 8.26050u − 3.19936
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
2168619486192
10770316588487
u
17
−
4825728074968
10770316588487
u
16
+ ··· +
588892268531920
10770316588487
u +
119654015108734
10770316588487
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
2
c
2
, c
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
2
c
3
(u
9
− u
8
+ 6u
7
− 3u
6
+ 15u
5
− u
4
+ 16u
3
− 4u
2
− 5u − 1)
2
c
4
, c
9
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
u
18
− 5u
17
+ ··· − 286u + 73
c
12
u
18
− 19u
17
+ ··· − 31208u + 5329
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
2
c
2
, c
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
2
c
3
(y
9
+ 11y
8
+ ··· + 17y −1)
2
c
4
, c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
2
c
6
, c
7
, c
8
c
10
, c
11
y
18
+ 19y
17
+ ··· + 31208y + 5329
c
12
y
18
− 41y
17
+ ··· + 388728668y + 28398241
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339672 + 0.982229I
a = −2.33238 + 1.39827I
b = −0.567186 − 1.241800I
3.90681 − 2.45442I −1.67208 + 2.91298I
u = 0.339672 − 0.982229I
a = −2.33238 − 1.39827I
b = −0.567186 + 1.241800I
3.90681 + 2.45442I −1.67208 − 2.91298I
u = 0.187418 + 1.191530I
a = 1.84537 − 1.63478I
b = −0.567186 + 1.241800I
3.90681 + 2.45442I −1.67208 − 2.91298I
u = 0.187418 − 1.191530I
a = 1.84537 + 1.63478I
b = −0.567186 − 1.241800I
3.90681 − 2.45442I −1.67208 + 2.91298I
u = −0.341082 + 1.161470I
a = 0.605538 + 0.751599I
b = 0.646857
4.48831 4.65235 + 0.I
u = −0.341082 − 1.161470I
a = 0.605538 − 0.751599I
b = 0.646857
4.48831 4.65235 + 0.I
u = 0.073821 + 1.217300I
a = 0.136037 − 1.077640I
b = −0.250475 − 0.120160I
1.50643 − 2.09337I −4.51499 + 4.16283I
u = 0.073821 − 1.217300I
a = 0.136037 + 1.077640I
b = −0.250475 + 0.120160I
1.50643 + 2.09337I −4.51499 − 4.16283I
u = −0.410768 + 0.428375I
a = −0.50504 + 1.49973I
b = −0.250475 + 0.120160I
1.50643 + 2.09337I −4.51499 − 4.16283I
u = −0.410768 − 0.428375I
a = −0.50504 − 1.49973I
b = −0.250475 − 0.120160I
1.50643 − 2.09337I −4.51499 + 4.16283I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35742 + 0.65746I
a = 0.610442 + 0.053041I
b = 1.01103 − 1.59917I
6.88799 + 7.08493I 1.57680 − 5.91335I
u = −1.35742 − 0.65746I
a = 0.610442 − 0.053041I
b = 1.01103 + 1.59917I
6.88799 − 7.08493I 1.57680 + 5.91335I
u = −1.22955 + 0.90859I
a = −0.408976 + 0.092875I
b = −0.01680 + 1.73270I
7.66122 + 1.33617I 3.28409 − 0.70175I
u = −1.22955 − 0.90859I
a = −0.408976 − 0.092875I
b = −0.01680 − 1.73270I
7.66122 − 1.33617I 3.28409 + 0.70175I
u = 0.00479 + 1.82789I
a = 0.090352 + 1.015340I
b = −0.01680 − 1.73270I
7.66122 − 1.33617I 3.28409 + 0.70175I
u = 0.00479 − 1.82789I
a = 0.090352 − 1.015340I
b = −0.01680 + 1.73270I
7.66122 + 1.33617I 3.28409 − 0.70175I
u = 0.23311 + 1.83083I
a = −0.137225 − 1.036180I
b = 1.01103 + 1.59917I
6.88799 − 7.08493I 1.57680 + 5.91335I
u = 0.23311 − 1.83083I
a = −0.137225 + 1.036180I
b = 1.01103 − 1.59917I
6.88799 + 7.08493I 1.57680 − 5.91335I
12
III.
I
u
3
= h−a
4
−a
3
u+a
3
+2a
2
u+4au+4b+4a−4, a
4
u−2a
3
u+· · ·+4a+4, u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
a
1
4
a
3
u −
1
2
a
2
u + ··· − a + 1
a
7
=
1
−1
a
3
=
1
4
a
3
u −
1
2
a
2
u + ··· −
1
4
a
3
+ 1
1
4
a
3
u −
1
2
a
2
u + ··· − a + 1
a
10
=
u
0
a
8
=
0
−1
a
9
=
−1
1
4
a
4
u −
1
2
a
3
u + ··· + a
2
+
1
2
a
a
12
=
−u
−
1
2
a
3
u + a
2
u + ··· +
1
2
a − 3
a
1
=
−u
−
1
2
a
3
u + a
2
u + ··· +
1
2
a − 3
a
2
=
1
4
a
4
u +
1
4
a
3
u + ··· + a
2
+ 3
3
4
a
3
u − 2a
2
u + ··· −
1
2
a + 2
a
5
=
−
1
4
a
4
u +
1
4
a
3
u + ··· +
1
4
a
3
−
1
2
a
2
−
1
2
a
4
−
3
4
a
3
u +
3
4
a
3
+ 2a
2
u + au + a − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
4
+ 2a
3
u − 2a
3
− 6a
2
u + 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
4
, c
9
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
(u
2
+ 1)
5
c
12
(u − 1)
10
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
4
, c
9
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
(y + 1)
10
c
12
(y −1)
10
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.794743 + 0.582062I
b = 1.41878 − 0.21917I
−2.58269 − 4.40083I −0.74431 + 3.49859I
u = 1.000000I
a = −0.582062 + 0.794743I
b = 1.41878 + 0.21917I
−2.58269 + 4.40083I −0.74431 − 3.49859I
u = 1.000000I
a = 0.821196 − 0.821196I
b = −1.21774
0.888787 2.51886 + 0.I
u = 1.000000I
a = 2.15793 + 0.60232I
b = −0.309916 + 0.549911I
2.96077 + 1.53058I 3.48489 − 4.43065I
u = 1.000000I
a = −0.60232 − 2.15793I
b = −0.309916 − 0.549911I
2.96077 − 1.53058I 3.48489 + 4.43065I
u = − 1.000000I
a = −0.582062 − 0.794743I
b = 1.41878 − 0.21917I
−2.58269 + 4.40083I −0.74431 − 3.49859I
u = − 1.000000I
a = −0.794743 − 0.582062I
b = 1.41878 + 0.21917I
−2.58269 − 4.40083I −0.74431 + 3.49859I
u = − 1.000000I
a = 0.821196 + 0.821196I
b = −1.21774
0.888787 2.51886 + 0.I
u = − 1.000000I
a = 2.15793 − 0.60232I
b = −0.309916 − 0.549911I
2.96077 − 1.53058I 3.48489 + 4.43065I
u = − 1.000000I
a = −0.60232 + 2.15793I
b = −0.309916 + 0.549911I
2.96077 + 1.53058I 3.48489 − 4.43065I
16
IV. I
u
4
= hb − 2a, 4a
2
+ 2a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
1
a
4
=
a
2a
a
7
=
1
1
a
3
=
3a
2a
a
10
=
1
2
a
8
=
2
3
a
9
=
1
2
a
12
=
−1
−1
a
1
=
−1
0
a
2
=
3a +
1
2
2a + 1
a
5
=
a
2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
31
2
a −
23
4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
9
u
2
c
6
, c
7
, c
8
(u − 1)
2
c
10
, c
11
, c
12
(u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
9
y
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.250000 + 0.433013I
b = −0.500000 + 0.866025I
−1.64493 + 2.02988I −1.87500 − 6.71170I
u = 1.00000
a = −0.250000 − 0.433013I
b = −0.500000 − 0.866025I
−1.64493 − 2.02988I −1.87500 + 6.71170I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
2
· (u
22
+ 10u
21
+ ··· − u + 16)
c
2
(u
2
+ u + 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
· (u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
2
· (u
22
+ 2u
21
+ ··· + 15u + 4)
c
3
(u
2
− u + 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
9
− u
8
+ 6u
7
− 3u
6
+ 15u
5
− u
4
+ 16u
3
− 4u
2
− 5u − 1)
2
· (u
22
− 2u
21
+ ··· + 663u + 676)
c
4
, c
9
u
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
· (u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(u
22
+ 3u
21
+ ··· + 120u + 32)
c
5
(u
2
− u + 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
2
· (u
22
+ 2u
21
+ ··· + 15u + 4)
c
6
, c
7
, c
8
((u − 1)
2
)(u
2
+ 1)
5
(u
18
− 5u
17
+ ··· − 286u + 73)
· (u
22
+ 2u
21
+ ··· + 11u
2
+ 1)
c
10
, c
11
((u + 1)
2
)(u
2
+ 1)
5
(u
18
− 5u
17
+ ··· − 286u + 73)
· (u
22
+ 2u
21
+ ··· + 11u
2
+ 1)
c
12
((u − 1)
10
)(u + 1)
2
(u
18
− 19u
17
+ ··· − 31208u + 5329)
· (u
22
− 30u
21
+ ··· − 22u + 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
2
· (y
22
+ 6y
21
+ ··· − 1857y + 256)
c
2
, c
5
(y
2
+ y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
2
· (y
22
+ 10y
21
+ ··· − y + 16)
c
3
(y
2
+ y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
9
+ 11y
8
+ ··· + 17y −1)
2
· (y
22
+ 2y
21
+ ··· + 1664143y + 456976)
c
4
, c
9
y
2
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
2
· (y
22
+ 5y
21
+ ··· − 1216y + 1024)
c
6
, c
7
, c
8
c
10
, c
11
((y −1)
2
)(y + 1)
10
(y
18
+ 19y
17
+ ··· + 31208y + 5329)
· (y
22
+ 30y
21
+ ··· + 22y + 1)
c
12
((y −1)
12
)(y
18
− 41y
17
+ ··· + 3.88729 × 10
8
y + 2.83982 × 10
7
)
· (y
22
− 78y
21
+ ··· + 102y + 1)
22
